1. On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization
- Author
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V. S. Amaral, R. Andreani, E. G. Birgin, D. S. Marcondes, and J. M. Martínez
- Subjects
Control and Optimization ,Optimization and Control (math.OC) ,Applied Mathematics ,FOS: Mathematics ,Business, Management and Accounting (miscellaneous) ,90C30, 65K05, 49M37, 90C60, 68Q25 ,Management Science and Operations Research ,Mathematics - Optimization and Control ,Computer Science Applications - Abstract
Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models for smooth nonconvex box-constrained minimization are introduced in this work. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with respect to all the variables simultaneously is $O(\varepsilon^{-(p+1)})$. Numerical examples involving multidimensional scaling problems are presented. The numerical performance of the methods is enhanced by means of coordinate-descent strategies for choosing initial points.
- Published
- 2022
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